Survival analysis applied to proportion data: comparing mammography visits in high and low repeat rate facilities

We examined the relationship between the proportion of time spent in the mammography exam room relative to the total visit time and the rate of repeat visits across mammography facilities. We hypothesized that the means for these proportions would be greater among facilities with high repeat rates compared to those with low repeat rates. The beta distribution was used to model the proportions. However, not all of the observations were observed as some were (right- or interval-) censored due to the inability to observe complete information (e.g., time of arrival at the facility) to calculate the proportions for some observations. Using a maximum likelihood approach, we estimated the mean proportion of time spent during appointments on the actual exams. To analyze these data we utilized survival analysis methods, which typically are applied to data on time scales, to analyze these data restricted to the range (0, 1). We found that facilities with high repeat mammography rates on average had a greater proportion of their visits spent receiving the exams than the low repeat rate facilities (p = 0.0003). Women from low repeat rate facilities spent on average 45 % of their appointment time engaging in the exam; thus, these women averaged more time waiting for the exam to begin than receiving the exam. Conversely, those from high repeat rate facilities averaged more of their appointment time engaging in the mammographic exams. These findings were consistent with our hypothesis that women would have greater satisfaction with their mammography appointments—and thus be more likely to return for routine screening—in facilities where their appointments were more efficient.